A univariate sieve density estimation based on a simulated Kolmogorov-Smirnov test

This paper proposes a simulated Kolmogorov-Smirnov (KS)-based sieve density estimation method. It exploits an objective function which is the difference of two empirical distribution functions, one involved with actual observations and the other with simulated observations. By minimizing the objective function with respect to the sieve parameters, a sieve density/distribution estimator is obtained. The equivalence of the sieve distribution estimator and the true distribution can be tested by the KS test since the KS test statistic is easily obtained from the objective function. The resulting sieve density estimator is shown to be consistent. Numerical experiments are conducted to verify the performance of the proposed method. Furthermore, the proposed method is applied to estimate the income density in South Korea. Whether the actual observations can be rationalized by the estimated distribution can be tested by the proposed bootstrap test.